Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment

In this article, free vibration and dynamic transient response of a multilayer polymer nanocomposite beam resting on elastic foundation reinforced by graphene platelets (GPLs) non-uniformly distributed through the thickness direction in thermal environment is investigated. Theoretical formulations are derived based on Hamilton's principle, Timoshenko beam theory relationships. The effective Young's modulus of the GPL/polymer composite is estimated by Halpin-Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies of the beam are obtained numerically by generalized differential quadrature method (GDQM). The influences of the distribution pattern, weight fraction, the number of layers, thermal environment, slenderness ratio of the beam, boundary conditions, and types of elastic foundations on the free vibration behavior and transient response are presented. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements together with the elastic foundation, significantly increases the natural frequencies of the beam. Placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the natural frequencies. Besides, with the increasing of foundation's stiffness, the displacement amplitude of the functionally graded composite beam reinforced by GPLs subjected to impulsive load decreases.

Automated summary

In this article, the free vibration and dynamic transient response of a multilayer polymer nanocomposite beam supported by an elastic foundation reinforced with graphene platelets (GPLs) are investigated in a thermal environment. The study presents theoretical formulations based on Hamilton's principle and Timoshenko beam theory relationships. The numerical results obtained using the generalized differential quadrature method (GDQM) show that adding a small amount of GPLs and placing more GPLs near the top and bottom surfaces of the beam effectively increases its natural frequencies. The influences of various factors on the vibration behavior and transient response are also presented.